I think you hit the nail on the head here.
By this point in time, most likely the Super Bowl opponent has more physical talent than the Patriots. This isn't a knock on the Patriots, it's a reality -- 1) Belichick has openly said in the past that he prefers someone who is selfless, knows and follows the system than someone slightly more talented who doesn't do that, and 2) the Patriots have not had "their own" 1st round draft pick better than pick 28 since the 2009 draft, and the Patriots do not normally chase after the marquee big-money free agent talent.
Their opponent is psyched to be in the Super Bowl, has spent 2 weeks game planning, and comes out guns ablazing. Scheming doesn't fully help in situations like this - especially when despite all that planning, you're finally learning what your opponent is actually going to do.
As the game goes on, that's when the Patriots' advantage starts to seep in. By then, they truly know what the opponent is trying to do so can adjust better, the opponent shot their load early and is now getting a bit tired while the well-conditioned Patriots keep bringing it to them, and sooner or later their coaches or players will mess up on what we consider fundamentals here -- clock management, penalty discipline, scheme discipline - that generally isn't tolerated here.
Factor all that in, and you get the Patriots slow starts, roaring finishes.